Interfacial thermodynamics of protein adsorption, ion co-adsorption and ion binding in solution. I. Phenomenological linkage relations for ion exchange in lysozyme chromatography and titration in solution

In this paper we discuss the thermodynamics of ion binding in solution, protein adsorption and ion co-adsorption. The emphasis is on charge regulation effects. To this end, we introduce phenomenological linkage relations from which the ion binding can be calculated from the electrolyte dependency of proton titration curves and the co-adsorption from the electrolyte dependency of protein adsorption isotherms. The linkage relations are derived from classical interfacial thermodynamics, and thus offer an alternative approach as compared to the mass balance equations which are currently used in biotechnology, and Record et al.'s 1978 analysis of Wyman's Binding Polynomial for protein interactions. The co-adsorption theory is an extension of our previous analysis of ion binding in solution, which we include here for comparison of the ion co-adsorption with the ion binding in solution. The theory is applied to the chromatography of lysozyme on the strong cation exchanger ‘mono S’ and to the proton titration of lysozyme in solution. In the accompanying Part 2 of this paper the results are interpreted with a simple model.